Geodesic
The Kramers–Wannier Symmetry and $S$-Duality in the Two-Dimensional $g\Phi ^4$ Theory
Teoretičeskaâ i matematičeskaâ fizika, Tome 131 (2002) no. 2, pp. 206-215 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

We show that the exact beta function of the two-dimensional $g\Phi ^4$ theory possesses two dual symmetries. These are the Kramers–Wannier symmetry $d(g)$ and the strong-weak-coupling symmetry, or the $S$-duality $f(g)$, connecting the strong- and weak-coupling domains lying above and below the fixed point $g^*$. We obtain explicit representations for the functions $d(g)$ and $f(g)$. The $S$-duality transformation $f(g)$ allows using the high-temperature expansions to approximate the contributions of the higher-order Feynman diagrams. From the mathematical standpoint, the proposed scheme is highly unstable. Nevertheless, the approximate values of the renormalized coupling constant $g^*$ obtained from the duality equations agree well with the available numerical results. 
@article{TMF_2002_131_2_a3,
     author = {B. N. Shalaev},
     title = {The {Kramers{\textendash}Wannier} {Symmetry} and $S${-Duality} in the {Two-Dimensional} $g\Phi ^4$ {Theory}},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {206--215},
     year = {2002},
     volume = {131},
     number = {2},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_2002_131_2_a3/}
}
TY  - JOUR
AU  - B. N. Shalaev
TI  - The Kramers–Wannier Symmetry and $S$-Duality in the Two-Dimensional $g\Phi ^4$ Theory
JO  - Teoretičeskaâ i matematičeskaâ fizika
PY  - 2002
SP  - 206
EP  - 215
VL  - 131
IS  - 2
UR  - http://geodesic.mathdoc.fr/item/TMF_2002_131_2_a3/
LA  - ru
ID  - TMF_2002_131_2_a3
ER  - 
%0 Journal Article
%A B. N. Shalaev
%T The Kramers–Wannier Symmetry and $S$-Duality in the Two-Dimensional $g\Phi ^4$ Theory
%J Teoretičeskaâ i matematičeskaâ fizika
%D 2002
%P 206-215
%V 131
%N 2
%U http://geodesic.mathdoc.fr/item/TMF_2002_131_2_a3/
%G ru
%F TMF_2002_131_2_a3
B. N. Shalaev. The Kramers–Wannier Symmetry and $S$-Duality in the Two-Dimensional $g\Phi ^4$ Theory. Teoretičeskaâ i matematičeskaâ fizika, Tome 131 (2002) no. 2, pp. 206-215. http://geodesic.mathdoc.fr/item/TMF_2002_131_2_a3/

[1] H. A. Kramers, G. H. Wannier, Phys. Rev., 60 (1941), 252 | DOI | MR | Zbl

[2] R. Savit, Rev. Mod. Phys., 52 (1980), 453 | DOI | MR

[3] J. B. Kogut, Rev. Mod. Phys., 51 (1979), 659 | DOI | MR

[4] S. G. Gukov, UFN, 168 (1998), 705 | DOI | MR

[5] B. N. Shalaev, Phys. Rep., 237 (1974), 129 | DOI | MR

[6] G. Jug, B. N. Shalaev, J. Phys. A, 32 (1999), 7249 | DOI | MR | Zbl

[7] G. Jug, B. N. Shalaev, FEChAYa, 31:7B (2000), 215

[8] A. I. Sokolov, E. V. Orlov, FTT, 42 (2000), 2087

[9] G. A. Baker (Jr.), B. G. Nickel, D. I. Meiron, Phys. Rev. B, 17 (1978), 1365 | DOI

[10] J. Zinn-Justin, Quantum Field Theory and Critical Phenomena, 3rd ed., Clarendon Press, Oxford, 1999 | MR

[11] H. B. Tarko, M. E. Fisher, Phys. Rev. B, 11 (1975), 1217 | DOI

[12] Shun-Yong Zinn, Sheng-Nan Lai, M. E. Fisher, Phys. Rev. E, 54 (1996), 1176 | DOI

[13] P. Butera, M. Comi, Phys. Rev. B, 54 (1996), 15828 | DOI

[14] P. H. Damgaard, P. E. Haagensen, J. Phys. A, 30 (1997), 4681 | DOI | MR | Zbl

[15] E. Barouch, B. M. McCoy, T. T. Wu, Phys. Rev. Lett., 31 (1973), 1409 | DOI

[16] P. Calabrese, M. Caselle, A. Celi, A. Pelissetto, E. Vicari, J. Phys. A, 33 (2002), 8155 ; E-print hep-th/0005254 | DOI | MR

[17] V. Privman, M. E. Fisher, Phys. Rev. B, 30 (1984), 322 | DOI | MR

[18] T. W. Burkhardt, D. Derrida, Phys. Rev. B, 32 (1985), 7273 | DOI

[19] A. LeClair, Phys. Rev. Lett., 84 (2000), 1292 | DOI